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Register a new userTopological states and interplay between spin-orbit and Zeeman interactions in a spinful Su-Schrieffer-Heeger nanowire
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The interplay between the spin-orbit and Zeeman interactions acting on a spinful Su-Schrieffer-Heeger model is studied based on an InAs nanowire subjected to a periodic gate potential along the axial direction. It is shown that a nontrivial topological phase can be achieved by regulating the confining-potential configuration. In the absence of the Zeeman field, we prove that the topology of the chain is not affected by the Rashba spin-orbit interaction due to the persisting chiral symmetry. The energies of the edge modes can be manipulated by varying the magnitude and direction of the external magnetic field. Remarkably, the joint effect of the two spin-related interactions leads to novel edge states that appear in the gap formed by the anti-crossing of the bands of a finite spinful dimerized chain, and can be merged into the bulk states by tilting the magnetic-field direction.
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In this paper we study the formation of topological Tamm states at the interface between a semi-infinite one-dimensional photonic-crystal and a metal. We show that when the system is topologically non-trivial there is a single Tamm state in each of the band-gaps, whereas if it is topologically trivial the band-gaps host no Tamm states. We connect the disappearance of the Tamm states with a topological transition from a topologically non-trivial system to a topologically trivial one. This topological transition is driven by the modification of the dielectric functions in the unit cell. Our interpretation is further supported by an exact mapping between the solutions of Maxwells equations and the existence of a tight-binding representation of those solutions. We show that the tight-binding representation of the 1D photonic crystal, based on Maxwells equations, corresponds to a Su-Schrieffer-Heeger-type model (SSH-model) for each set of pairs of bands. Expanding this representation near the band edge we show that the system can be described by a Dirac-like Hamiltonian. It allows one to characterize the topology associated with the solution of Maxwells equations via the winding number. In addition, for the infinite system, we provide an analytical expression for the photonic bands from which the band-gaps can be computed.
The Su-Schrieffer-Heeger (SSH) model on a two-dimensional square lattice has been considered as a significant platform for studying topological multipole insulators. However, due to the highly-degenerate bulk energy bands protected by $ C_{4v} $ and chiral symmetry, the discussion of the zero-energy topological corner states and the corresponding physical realization have been rarely presented. In this work, by tuning the hopping terms to break $ C_{4v} $ symmetry down to $ C_{2v} $ symmetry but with the topological phase invariant, we show that the degeneracies can be removed and a complete band gap can be opened, which provides robust protection for the spectrally isolated zero-energy corner states. Meanwhile, we propose a rigorous acoustic crystalline insulator and therefore these states can be observed directly. Our work reveals the topological properties of the robust zero-energy states, and provides a new way to explore novel topological phenomena.
Topological physics strongly relies on prototypical lattice model with particular symmetries. We report here on a theoretical and experimental work on acoustic waveguides that is directly mapped to the one-dimensional Su-Schrieffer-Heeger chiral model. Starting from the continuous two dimensional wave equation we use a combination of monomadal approximation and the condition of equal length tube segments to arrive at the wanted discrete equations. It is shown that open or closed boundary conditions topological leads automatically to the existence of edge modes. We illustrate by graphical construction how the edge modes appear naturally owing to a quarter-wavelength condition and the conservation of flux. Furthermore, the transparent chirality of our system, which is ensured by the geometrical constraints allows us to study chiral disorder numerically and experimentally. Our experimental results in the audible regime demonstrate the predicted robustness of the topological edge modes.
The interplay between Rashba, Dresselhaus and Zeeman interactions in a quantum well submitted to an external magnetic field is studied by means of an accurate analytical solution of the Hamiltonian, including electron-electron interactions in a sum rule approach. This solution allows to discuss the influence of the spin-orbit coupling on some relevant quantities that have been measured in inelastic light scattering and electron-spin resonance experiments on quantum wells. In particular, we have evaluated the spin-orbit contribution to the spin splitting of the Landau levels and to the splitting of charge- and spin-density excitations. We also discuss how the spin-orbit effects change if the applied magnetic field is tilted with respect to the direction perpendicular to the quantum well.
We address the conditions required for a $mathbb{Z}$ topological classification in the most general form of the non-Hermitian Su-Schrieffer-Heeger (SSH) model. Any chirally-symmetric SSH model will possess a conjugated-pseudo-Hermiticity which we show is responsible for a quantized complex Berry phase. Consequently, we provide the first example where the complex Berry phase of a band is used as a quantized invariant to predict the existence of gapless edge modes in a non-Hermitian model. The chirally-broken, $PT$-symmetric model is studied; we suggest an explanation for why the topological invariant is a global property of the Hamiltonian. A geometrical picture is provided by examining eigenvector evolution on the Bloch sphere. We justify our analysis numerically and discuss relevant applications.
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